Ambient spaces of dimensional dual arcs
Generalizing the family of 1-dimensional subspaces namely of the tangents of an arc a \(d\)-dimensional dual arc in a finite projective space \(PG(n,q)\) is defined. Those of maximal cardinality are called dual hyperovals and those dual arcs which are not part of a bigger one are called complete dual arcs. The author is only interested in the case \(d>1\). He asks for an upper bound on \(n\) given \(d\) and \(q\). It is shown that for dual hyperovals and a lot of smaller subsets in the case \(q\neq 2\) one has \(n\geq d(d+3)/2=:D\) and that this bound is best possible. In the last part the author constructs \(d\)-dimensional dual arcs in connection with quadric Veroneseans in \(PG(D,q)\).
scientific article; zbMATH DE number 2081995